Total Internal Reflection: Light Trapped in Water
#Presented by Anirudh
Introduction
#When light passes from one transparent material into another — say, from water into air — it bends at the boundary. This bending is called refraction, and it is responsible for the way objects look displaced when viewed through a water surface, and for the way lenses focus light. But refraction has a surprising limit: if the light inside the denser material hits the boundary at too steep an angle, it cannot pass through at all. Instead, it bounces straight back, as if the boundary were a perfect mirror. This is total internal reflection.
In this demonstration, a large clear plastic bottle filled with water is placed on a rotating stand. A laser pointer is shone into the bottle from outside. As the angle at which the light strikes the curved wall of the bottle is varied by rotating the bottle, the audience can watch the transition: at shallow angles the light passes through and continues into the air beyond; at steeper angles, beyond a sharply defined threshold called the critical angle, the light stops escaping and bounces back entirely within the water. The same principle is at work in optical fibres, which carry the internet around the world by keeping light trapped inside a glass core using exactly this effect.
Precautions
#Never shine the laser directly into anyone's eyes — even a low-power laser pointer can cause eye damage. Aim the beam at the bottle only, and warn bystanders to look at the bottle rather than at the beam. Ensure the bottle is filled completely and has no large air bubbles, which would disturb the internal reflections. A darkened room makes the effect much easier to see.
Materials Required
#- A large clear plastic bottle (2 L) filled with clean water
- A small laser pointer or narrow-beam torch
- A rotating turntable or lazy-susan to allow the bottle angle to be changed smoothly
Science Behind It
#When light crosses from a medium with refractive index n₁ into one with index n₂, its direction changes according to Snell's law: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ is the angle of incidence and θ₂ is the angle of refraction, both measured from the normal to the surface. For light going from water (n₁ ≈ 1.33) into air (n₂ = 1.00), the refracted ray bends away from the normal: since n₁ > n₂, the transmitted ray is always at a steeper angle to the surface than the incoming ray.
This has a consequence: as θ₁ increases, θ₂ rises faster, and there comes a point where θ₂ would need to equal 90° — meaning the refracted ray would run along the boundary surface itself. The angle of incidence at which this happens is the critical angle, θ_c, given by sin θ_c = n₂/n₁ = 1/1.33 ≈ 0.75, so θ_c ≈ 48.8° for the water–air interface. For any angle of incidence greater than θ_c, Snell's law has no solution: no refracted ray exists in air, and all the light is reflected back into the water. The transition from partial reflection to total reflection happens sharply at this critical angle, which is why the laser beam visibly switches from passing through the bottle wall to bouncing back inside it.
The reflectance at total internal reflection is exactly 100%, making it more efficient than any metal mirror — no silvering or coating needed, and no absorption. Optical fibres exploit this by constructing a glass fibre whose core (higher refractive index) is surrounded by a cladding (lower refractive index). Any light ray entering the core at a shallow enough angle propagates the entire length of the fibre, bouncing between the walls by total internal reflection with very little loss even around bends. Modern telecommunications infrastructure — carrying voice calls, video, and internet traffic across continents — depends entirely on this principle.